How to ace the brain teaser interview (2005 mcgraw hill)

Tổng hợp các kỹ năng giúp bạn làm hồ sơ và phỏng vấn việc làm tốt.Tài liệu không thể thiếu cho sinh viên mới ra trường.

Reason: I attest to the accuracy and integrity of this document Date: 2005.07.04 23:45:43 +08'00'

Want to learn more?

We hope you enjoy this McGraw-Hill eBook! If you’d like more information about this book, its author, or related books and websites, please click here.

HOW TO ACE THE BRAINTEASER INTERVIEW

form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher

0-07-144606-0

The material in this eBook also appears in the print version of this title: 0-07-144001-1

All trademarks are trademarks of their respective owners Rather than put a trademark symbol after every occurrence of

a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no tion of infringement of the trademark Where such designations appear in this book, they have been printed with initial caps

inten-McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs For more information, please contact George Hoare, Special Sales, at george_hoare@mc- graw-hill.com or (212) 904-4069

TERMS OF USE

This is a copyrighted work and The McGraw-Hill Companies, Inc (“McGraw-Hill”) and its licensors reserve all rights

in and to the work Use of this work is subject to these terms Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, mod- ify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part

of it without McGraw-Hill’s prior consent You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited Your right to use the work may be terminated if you fail to comply with these terms

THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR RANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IM- PLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE McGraw-Hill and its licensors do not warrant or guarantee that the functions con- tained in the work will meet your requirements or that its operation will be uninterrupted or error free Neither McGraw- Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom McGraw-Hill has no responsibility for the content of any information accessed through the work Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, in- cidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even

WAR-if any of them has been advised of the possibility of such damages This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise

DOI: 10.1036/0071446060



CONTENTS

Chapter 9 Gross Order of Estimation Problems 181

Puzzles 128–141

Puzzles 142–152

Appendix A: Facts You Should Know 211

Appendix B: 20 Think-on-Your-Feet Questions 213

Appendix C: Additional Fermi Problems 215

Appendix D: Puzzles Inappropriate for Job Interviews 219

Appendix E: Additional Sources and Links 225

List of Problems 235

PREFACE

Here’s a brainteaser for you

Why do employers subject already nervous job candidates to teasers, puzzles, business cases, and other mind-benders? Do suchpuzzles really help employers build teams of highly logical, curious,successful, hard-working, motivated contributors who can be expected

brain-to hit the ground running?

Hardly anyone believes that There are no studies that give scientificsupport to the notion that success at brainteasers and logic puzzlespredicts success at the job So if employers know that, why do inter-viewers persist in using valuable job interview time for this peculiar style

inter-By giving candidates good puzzles you get a fair estimate of how smartthey are, and the discussion gives you some interaction with the candi-date, too.”

With the downturn in the tech sectors, more and more people are ing fewer jobs Interviewers are often faced with hundreds of résumésfor one position When all these candidates seem exceptionally qualified

chas-v

for the job, how is the interviewer to select? Using brainteasers and puzzlesmakes sense at companies that focus recruitment efforts more on whatcandidates might do in the future than on what they have done in the past.These companies understand that in today’s fast-paced global businessworld, specific skills are of limited use because technology changes soquickly What is really needed, interviewers believe, are curious, obser-vant, quick-witted candidates who welcome new challenges, demonstratemental agility under stressful conditions, learn quickly, defend theirthinking, and demonstrate enthusiasm for impossible tasks

It also doesn’t hurt that Microsoft, the most successful company of alltime, is known to add brainteasers to the mix of interview questions itasks the thousands of super-bright candidates who come knocking atits gates No human resources director has ever been fired for aligninghis or her company’s hiring practices with Microsoft’s

PUZZLES AND BRAINTEASERS IN ACTION

Joel Spolsky, president of New York–based Fog Creek Software, stands that brainteasers or other challenges are a critical part of the inter-view process because they help narrow the large number of “maybes” thatcrowd any job search “There are three types of people in the softwarefield,” notes Spolsky, who got his first job at Microsoft “At one end ofthe scale, there are the unwashed masses, lacking even the most basicskills for the job.” They are easy to ferret out and eliminate, often just byreviewing a résumé and asking two or three quick questions At the otherextreme are the superstars who write compilers for fun “And in themiddle, you have a large number of ‘maybes’ who seem like they mightjust be able to contribute something,” Spolsky adds

under-At Fog Creek, brainteasers are used to identify candidates who notonly are smart, but who get things done “Our goal is to hire people

with aptitude, not a particular skill set,” Spolsky says “Smart is tant, but hard to define; gets things done is crucial In order to be able

impor-to tell, you’re going impor-to have impor-to ask the right questions.”

The brainteaser challenge comes after Spolsky establishes rapportwith the candidate, asks about skills and projects, and poses some be-havioral questions (“Tell me about a time when you faced a deadlinecrunch ”) The first thing Spolksy looks for in a candidate is passion

After that, he gives the candidate an impossible gross-order estimationquestion “The idea is to ask a question that they have no possible way ofanswering, just to see how they handle it,” he says How many optometristsare there in Seattle? How many tons does the Washington Monumentweigh? How many gas stations are in Los Angeles? More of these puzzlescan be found in Chapter 9.

“What an applicant knows gets him or her through the first interview,”says Ed Milano, vice president of Marketing and Program Development

at Design Continuum, a product design consulting firm with offices inBoston, Milan, and Seoul By the time the applicant gets to Milano, apti-tude and experience are not in question For Milano to make a job offer,

he has to see how the applicant thinks under stressful conditions, theenvironment that often describes life at a consultancy that assists clientswith make-or-break strategic design programs

Ed Milano, like many recruiters, has often found that starting an view with a brainteaser is effective Logic puzzles have a long tradition

inter-in fast-movinter-ing high-tech companies where beinter-ing quick on your feet is

an asset As the rest of the world has embraced the attributes of the moving, ever-wired, start-up mentality of the high-tech computer company,many recruiters are adopting the in-your-face style of interviewingassociated with technology-intensive start-ups Some recruiters earnestlybelieve that brainteasers are valid tools to gauge the creativity, intelli-gence, passion, resourcefulness, etc., of candidates Others are willing

fast-to accept that puzzles are little more than interview stunts that may ormay not reveal aspects of the candidate’s character and may actuallyalienate some candidates In any case, brainteasers are here to stay

A reasonable question readers often ask me is, “Given that this bookhas now published these brainteasers and their solutions, why would anyinterviewer ever use these brainteasers again?”

Let me give two answers First, interviewers love candidates whohave prepared for interviews They want you to prepare The fact is,there are literally hundreds of Web sites that discuss these puzzles,sometimes with solutions, sometimes not Besides, many of these brain-teasers don’t have solutions And of the puzzles that do, interviewersunderstand, as you should, that reading the solutions to these puzzles is

no substitute for understanding them and being able to carry on an

intelligent conversation And intelligent conversation—what thesebrainteasers are designed to catalyze—can’t be faked.

Second, there are dozens of interviewing books that prep candidates

on such staples of the job interview as “Where do you want to be in fiveyears?” and “What’s your greatest weakness?” but interviewers still askthose questions You can buy this book with confidence The next job in-terview brainteaser you are asked is likely to be discussed within thesepages

Good luck on acing the brainteaser job interview

JOHNKADOR

Geneva, Illinois

My gratitude goes, first, to those who advised me not to write this book.Some very smart people argued that it is neither valid nor moral to makebrainteasers a part of the job selection process, but in making their casethey contributed some very juicy brainteasers that made their way intothis book Whether we like it or not, job interview brainteasers are outthere and we should be prepared As Trotsky said, “You don't have tobelieve in street cars to take them where you want to go.”

Dozens of other veterans of the brainteaser wars, not all of whomwant to be named here, helped me compile these puzzles and their solu-tions The brainteasers themselves were offered with generosity Thepreferred solutions were held in greater confidence, and I am mostgrateful to those who occasionally bent a company policy or two toshare their insights with me I also acknowledge the workers who re-counted their often exasperating experiences with brainteasers in thecontext of tension-filled job interviews Whether they operate on oneside of the interviewing table or the other, I am grateful to the followingindividuals who permitted me to mention their names: Peter Alkemade,Adam Barr, Phil Brady, Dale Fedderson, Robert Gately, Tom Gentry,Vikas Hamine, Charles Handler, Pete Herzog, Ben Kovler, Carl Kutsmode,Marie Lerch, Steve Levy, Joe Mabel, Bill McCabe, Ed Milano, ScottSchoenick, Kevin Stone, Koen Van Tolhuyzen, Kevin Wheeler, JeffreyYamaguchi

Scores of Web logs (blogs) focus on the job interview process atMicrosoft and other high-tech companies A number of bloggers helped

me define this book and invited their readers to contribute puzzles and sonal experiences This book is richer for their efforts I would especially

per-i x

like to acknowledge the following individuals: Vicki Brown, Ole Eichorn,Ron Jacobs, Johanna Rothman, Chris Sells, Joel Spolsky, and JeffreyYamaguchi Links to their blogs may be found in Appendix E.

Mr Micah Fogel, an instructor in the math department at Illinois Mathand Science Academy in Aurora, Illinois, agreed to recruit a couple

of his top math students to review the puzzles in this book IMSA(www.imsa.edu) is an elite, residential high school that attracts academ-ically gifted students from throughout Illinois I am indebted to Micahand his excellent students, Letian Zhang and Xi Ye, for making severalsuggestions that spared this book of critical lapses in logic and rigor.Finally, I am grateful to my friends and associates in Illinois who tol-erated my insistent pestering on questions of wording and meaning.Roger Breisch, a good friend who once taught high-school mathematics,was generous in reviewing my equations and proofs; Roger invariablyimproved both I am also grateful to Barry Glicklich, Katherine Lato,Dan Kador, Elizabeth Nelson, and David W Jones for critical contributions

to selected puzzles Any errors, misstatements, or omissions in the entation and unraveling of these puzzles, then, are entirely my own

pres-TO THE READER

If you are in the job market—particularly pursuing jobs in high tech,consulting, finance, insurance, and manufacturing—this book is for you.This book presents the largest collection of the actual puzzles, brain-teasers, and mind-benders being used by interviewers and recruiters aroundthe world Many puzzles are printed here for the first time With eachpuzzle is a discussion of not only the solution, but—more important—the quality of responses that interviewers find most compelling The book includes many of the most common puzzles and brainteasersused by Microsoft and companies in other industries Many of the puzzlesselected for this book were nominated by interviewers, recruiters, andstaffing professionals who use them on a day-to-day basis Others camefrom candidates themselves For the most part, organizations are noteager to have the puzzles they use in job interviews exposed For thatreason, many of the people who have cooperated with me in assemblingthese puzzles have asked that their names not be used I have respectedthose requests

James Fixx, author of Games for the Superintelligent and other puzzle

books, offers this advice for people with puzzles to solve: “One way toimprove your ability to use your mind is simply to see how very brightpeople use theirs.” The following pages detail how hundreds of verysmart people have solved the puzzles and brainteasers that other very smartpeople have given them In his puzzle books, Fixx valiantly tries to explainwhat, as he so delicately puts it, “the superintelligent do that’s differentfrom what ordinary people do.”

Fixx advises people to think hard and loose and to see the problem

at a slant “The true puzzler gropes for some loophole, and, with

x i

luck, quickly finds it in the third dimension.” Further hints abound: “Theintelligent person tries not to impose unnecessary restrictions on hismind.” Fixx admires determination: “The bright person has succeededbecause he does not assume the problem cannot be solved simplybecause it cannot be solved in one way or even two ways he has tried.” Here’s the paradox The candidates whose solutions are described inthis book recognize that the flashes of insight that Fixx describes, andthat interviewers expect of job candidates, are more a result of intuitionthan rigorous logic “What is particularly troubling is how little ‘logic’seems to be involved in some phases of problem solving Difficult prob-lems are often solved via a sudden, intuitive insight One moment you’restuck; the next moment this insight has popped into your head, thoughnot by any step-by-step logic that can be recounted.” But whatever it is—out-of-the-box thinking, third-eye vision—it’s clear that interviewerswant it

This book is primarily intended for job seekers You don’t have time towaste, so let’s get down to the question job seekers deem most impor-tant Can this book really help me ace the brainteaser job interview?Stated another way:

Will studying help me ace the brainteaser job interview?

The answer is yes The mind is a muscle Creative, flexible thinking can

be improved by exercise, and systematically working the logic puzzles

in this book can serve as the basis for training The strategic goal is tomake creative thinking a lifelong habit The first step is to become famil-iar with the norms, conventions, and traps of logic puzzles Workingthe puzzles in this book can be a way to start At a minimum, you won’t

be completely taken aback when you are confronted with one Perhapsyou may even be given one of the puzzles you have studied—and thenyou have a moral choice to make

Perhaps the biggest benefit of working the puzzles in this book is totrain your brain against betraying you when you need it the most Most

of these puzzles feature traps that exploit the laziness of our brains Ourbrains make thousands of assumptions—rote assumptions—everyminute just so we can get through the day Imagine if we had to consciously

analyze every action we take Logic puzzles exploit this property of ourbrains by sneaking under the radar of our assumptions Or they findwormholes in our pattern recognition.

The intelligence these puzzles seek to reveal calls on your ability tochallenge rote assumptions, see patterns where they exist, and rejectthem where they don’t To solve these puzzles, you have to questionyour usual ways of thinking, brainstorm new approaches, and evaluatethose new approaches critically—and those skills can be honed by simplyworking the puzzles in this book

Most logic puzzles and brainteasers exploit a relatively small number

of booby traps, psychological tricks, missing information, and otherswindles that penalize the would-be solver The good news is that there

is often a “trick” to solving these problems See Chapter 2 for a scription of these mental tricks and shortcuts Sometimes it’s as easy asrealizing that some critical information is missing Other times it’s therealization that your brain has filled in a missing piece of information—but filled it in incorrectly If you know the trick or can quickly detect

de-it, you will be in a much stronger position and avoid the dead ends thepuzzles are designed to take you down That in itself can give youthe confidence to take the puzzle, even if you have never heard it before,

to the next level

If you want to study, a focused course in psychometrics—the study ofmeasuring human abilities—might be helpful A job interview is justanother form of testing Interviewers expect that the job candidates’responses to specific questions provide some useful clues about out-comes Mostly, the responses don’t, but no one has figured out a betterway to select employees

A WORD TO INTERVIEWERS AND RECRUITERS READING THIS BOOK

While this book is primarily written for job candidates, interviewers andrecruiters will also find much benefit in these pages If you currently usepuzzles and brainteasers in your interviews, you will certainly increaseyour repertoire and perhaps find puzzles more appropriate to yourstaffing assignments Even if many of these puzzles are familiar, perhaps

the discussion of the solutions will increase your perspective about theirimplications If you are not currently using puzzles and brainteasers, thisbook may introduce you to the value of adding selective puzzles to themix of questions The following guidelines, based on research with hun-dreds of recruiters and candidates, may help you get maximum benefitout of these questions and avoid some mistakes

Try to select puzzles that have some relevance to the job and the dates’ real-world business performance There is a correlation betweenspecific puzzles and real-world skill sets called on by specific jobs becausemany of the cognitive skills needed are the same For example, select-ing candidates for a job that requires aptitude in strategic planning could

candi-be advanced by giving candidates puzzles that call on their strategicplanning capacities A search for a product manager who would berequired to make a series of high-risk bets on incomplete evidence could

be advanced by the use of puzzles testing quick decision-making andprobability skills The bottom line is, try to make the puzzle fit the job

“I prefer puzzles with layers, where there isn’t a ‘right’ answer, ormaybe where there is one answer which is relatively obvious, and an-other which is deeper,” insists Ole Eichorn, CTO of Aperio Technologies

“Good puzzles are solvable Perhaps the biggest problem with manyinterview puzzles is that they’re too hard If good, smart candidates can’tsolve them, they aren’t useful In addition, ideal puzzles involve steadythinking and problem solving rather than an ‘aha’ insight,” he adds.Should you be concerned that candidates have heard puzzles before?Not really You should expect that the best candidates have prepared for thejob interview But just because they have prepared an answer for questionssuch as “Tell me about a time when you solved a difficult problem?” doesthat mean there’s no value in your asking it? By the same token, the bestpuzzles are the ones that depend less on a specific solution and more

on reasoning There may be one “correct” answer, but many ways ofgetting there Or there may be an unlimited number of solution sets, andthe fun is in exploring a handful of them The point is to use the puzzle

as the basis of a conversation While a candidate may have memorized

a puzzle and can go through the motions, a good verbal presentation isdifficult to counterfeit

PUZZLES AND BRAINTEASERS GUIDELINES FOR USE

Based on feedback from dozens of interviewers, recruiters, and staffingprofessionals, here are some rules and guidelines for the use of puzzlesand brainteasers in job interviews:

1 Test, test, test Always try out a puzzle on colleagues, friends, and the

guys at the health club before using it in a job interview Never use acandidate to test a puzzle for the first time

2 Know the puzzle inside and out Never give a puzzle that you don’t

thor-oughly understand Knowing the “right answer” is not enough Youneed to have a deep understanding of the puzzle and every likely solu-tion set, correct or incorrect, and you need to know how to guide thecandidate through the puzzle You are guaranteed to encounter can-didates who understand the puzzle more deeply than you do Don’tembarrass yourself and the candidate

3 Make it win-win Job interview puzzles must be win-win That is, they

must not defeat the candidate Some candidates will nail the puzzle,and others will need help That’s okay But don’t let a candidate goaway feeling defeated or, worse, cheated Let every candidate emergefeeling like a victor Ideally, the puzzle will be a learning opportu-nity for both parties and, in the best cases, even fun In other words,you need to practice having a meaningful conversation about thechallenge

4 If in doubt, don’t If you’re not absolutely sure about a puzzle or

brainteaser, don’t even think about using it Never just throwpuzzles at candidates and see what sticks Make sure you under-stand what information you are looking for and how you will usethe results

5 At least one solution Don’t ask candidates to solve a puzzle that does

not have a solution It’s okay, even preferred, for puzzles to have morethan one solution, but it must have at least one satisfying conclusion

Be aware of the power differential in a job interview Asking a didate to consider a puzzle that is impossible to solve is nothing lessthan a trap

can-HOW THIS BOOK IS ORGANIZED

How to Ace the Brainteaser Interview organizes puzzles by category and

difficulty Starting with Chapter 3, the book deals with puzzles that,when all is said and done, have at least one preferred answer Chapter 3—

“Real-World Reasoning Puzzles”—includes puzzles that deal with cepts in physics and everyday objects Chapter 4 has logic puzzles that

con-do not require math more onerous than counting Chapter 5, on the otherhand, has more than two dozen logic puzzles that call on some skill inelementary arithmetic, algebra, and geometry Chapter 6 includes somedelightful puzzles that require at least some familiarity with probabilitytheory Chapter 7 has puzzles that are appropriate for programmers andanalysts, and these puzzles require basic programming concepts for theirsolutions

But many puzzles really don’t have an answer, or if they do, no onecares what they are These puzzles are about process—the steps the can-didate takes to bring the puzzle to some satisfactory resolution—andthese puzzles are the subject of Chapters 8 to 10 Many of these types

of puzzles show up in the business case interviews favored by consultingfirms Chapter 8 lists some of the more common business cases now mak-ing the rounds Chapter 9—“Gross Order of Estimation Problems”—features puzzles such as “How many piano tuners are there in America?”and other so-called Fermi problems Chapter 10—“PerformancePuzzles”—includes puzzles that actually require a candidate to get upand perform some activity, such as “sell me this pen.”

This book presents 152 brainteasers and puzzles Each brainteaserstarts with an introduction and a statement of the puzzle Most brain-teasers include a hint that interviewers have been known to offer candidateswho need a bit of help The critical part of each puzzle is a discussion

of the “aha!” opportunity as well as the booby traps and other land minesthat trip up unwary candidates The discussion of each puzzle includesadvice on how to overcome these traps and provides a statement of thesolution and alternative solutions, if any To ground the book in reality

as much as possible, the actual responses that interviewers deemed mostoutstanding are included whenever available In some cases, the bookdiscusses an extra credit variant of the puzzle and its solution to makeyou look even more perceptive

RIDDLE ME THIS

Interviewers are looking for meaningful, uncontroversial conversationswith candidates that will provide actionable information on which tomake reliable selection decisions Interviewers hope that puzzles andbrainteasers will help create the possibility of such quality conversations.Joel Spolsky, founder of Fog Creek Software and a former programmanager at Microsoft, is an advocate of using brainteasers, primarily

as conversation starters “The goal is to have an interesting conversationwith the candidate, and to use that conversation to see how smart andcapable they are,” Spolsky explains “If you have an interesting conver-sation about certain types of topics with a person, you can determine if[he] is the type of person you want to hire The questions are almost apretext to having that conversation.”

In almost all cases, the interviewers are less interested in the answeryou offer than in the road you use getting there It’s all about process Tothat extent, the best strategy is to take your time, think out loud, and letthe interviewer see you sweat (at least a little) Ironically, solving thesepuzzles too fast may work against you At a minimum, the interviewermay conclude you’ve heard the puzzle before In any case, even if youimpress the interviewer with your speed, you will have missed the oppor-tunity to talk about how you would use the skills you just demonstrated

to add value to the company Let the interviewer participate with you insolving the puzzle

The truth is, puzzles generally make up less than 10 percent of anyjob interview “The puzzles are a small part of the interview process atMicrosoft,” says Ron Jacobs, product manager for the Platform Architec-ture Guidance Team “We’ve found it’s very effective in giving us insight

1

into a candidate’s potential And that potential is the hardest thing togauge We know the résumé looks good, and they seem to have the skills.These puzzles put them in a place where it’s just them and their rawthinking abilities.”

Jacobs says that the puzzles are usually designed so that there are noclear answers Sometimes the interviewer will throw a candidate a hintthat points to a solution that is clearly wrong, just to see how the candidatewill defend his or her position and push back “A level of confidence isgood,” Jacobs says “Microsoft is very much a company that values thatkind of independent thought.” But don’t let the attitude slip into stubborn-ness or arrogance, he adds

Jacobs speaks from experience He should know, because he’s hadthree interviews at Microsoft In 1997, in his first time at bat, Jacobsimpressed people that he was a “Microsoft hire,” but he was neverthelessthought not a good fit for the position at hand In his first interview,

he was asked to design an airport Jacobs immediately began to waxeloquent about how he would design a world-class international airportlike Seattle’s SeaTac or Chicago’s O’Hare But after letting Jacobs go onfor five minutes, the interviewer stopped him and said, “But all I need

is a small regional airport.” Jacobs learned a lesson: “I didn’t clarify cisely what the customer needed.”

pre-In his second interview a year later, Jacobs anticipated brainteasersbut didn’t get any He was asked to solve a coding problem instead.Since then, he’s interviewed for an internal job “My take on the big pic-ture here is that when we ask these questions we are looking not somuch for the answer, but how the candidate thinks about the problem andapproaches the solution,” Jacobs notes “Some candidates will be veryquiet for a few minutes and then spew out an answer This is generally

a bad approach,” he says “A better approach is for candidates to thinkout loud as though they were collaborating with me on the answer I es-pecially like to hear them ask questions which clarify the problem.Sometimes we will ask an intentionally vague question to test for this.”

THE INTERVIEWER’S DILEMMA

Selectivity is the key reason for interviewers including puzzles in the mix.Interviewers believe that puzzles help them separate the outstanding

candidates from the great ones Ironically, a recession that creates a seller’smarket (more candidates applying for each job) only aggravates the inter-viewer’s dilemma Selectivity becomes harder, not easier, when dozens

or even hundreds of candidates chase each position Now interviewersare confronted with an abundance of outstanding candidates who allseem perfectly suited to the requirements of the job Each has passedthe preemployment background screening and sports a sterling résumé, therequisite technical skills, the appropriate certifications Pastures of plenty!It’s easy to distinguish between an average performer and a superstar.But what do you do when you have to select among superstars? You may have noticed that the job reference, once the backbone ofany recruitment process, is nowhere mentioned Over the past 25 years,organizations have become increasingly reluctant to provide references forformer employees The reluctance is not hard to understand In our litigioussociety, job applicants—whether downsized or voluntarily separated—have their attorney’s telephone number on speed dial, ready to push thebutton for any perceived slight As a result, most organizations will limitreference checks to verifying dates of employment and job title and finalsalary at separation An increasing number of companies automate thereference-checking process using touch-tone voice-response systems toeliminate the chance that a human might say something that a formeremployee can claim was defamatory

Letters of reference, once key to the hiring process, are likewise lete Even on the rare occasions when they are submitted, reference-letterinflation makes them less useful Every reference is glowing; every appli-cant is flawless If they were so flawless, interviewers rightly wonder, whyare they unemployed? No one wants to take the risk of writing a letterthat is nuanced Besides, with many candidates applying through theInternet, there’s often no opportunity to submit letters or attachments

obso-of any kind

Today, even the traditional job interview—the most valuable tool indeciding on the “fit” of a potential employee—is circumscribed Inter-viewers are running scared Interviewers now have to worry about subjects

they need to avoid and questions they are not allowed to ask In the United

States, state and federal law take a whole swath of topics and questionsoff the table Interviewers are not supposed to ask a candidate’s age,

weight, marital status, ethnicity, national origin, citizenship, politicaloutlook, sexual preference, financial status, or reproductive plans Exceptfor specific jobs, interviewers can’t even ask about a candidate’s arrestrecord Only questions that point to the candidate’s ability to do the job athand are allowed Many of these rules protect women and minorities,and that’s good No one wants to go back to the days when employersasked women job applicants about their birth control practices But thenew rules also create uncertainty about the kind of small talk that is vitalfor any human interaction Innocent questions such as, “Did you havetrouble getting here?” become ominous when the interviewer is afraidthat the candidate may wonder if the question is just an icebreaker or

an attempt to discover if the candidate drove or took the bus

For these reasons and more, puzzles and brainteasers are making acomeback Employers are desperate It’s all part of an increasing empha-sis to use the job interview to provide actionable information on which

to make reliable judgments With many job interview questions off thetable, puzzles and brainteasers become more attractive as a way to haveextended conversations with candidates By asking candidates to respond

to a puzzle or brainteaser, the conversations not only stay on safe ground,but create an opportunity to have a conversation that genuinely revealscritical aspects of how the candidate approaches a challenge, formulates

a response, and articulates a strategy When most of the candidates onthe short list are overqualified for the position, these types of conversa-tions, interviewers hope, can give them a meaningful basis on which tomake a selection

PUZZLES THAT WORK

Puzzles appropriate for job interviews help catalyze a meaningful sation between the candidate and the interviewer It is in this conversation,more than the solution to any particular puzzle, that the value of the inter-view is experienced

conver-The world is full of puzzles, but relatively few of them are appropriatefor job interviews Most, for one reason or another, simply don’t createextended conversations (see Appendix D for types of puzzles inappro-priate for job interviews) The puzzles that have the best possible tractionfor interviews have these attributes:

• Have solutions Puzzles are meant to be solved.

• Short The puzzle statement is clean, crisp, and obvious Puzzles with

elaborate narrations or many conditions don’t work well The bestpuzzles can be solved in less than five minutes, although the conver-sations about them can be extended

• Open ended Puzzles that have multiple acceptable answers allow

candidates to be creative or demonstrate their ability to come up withmultiple solutions Most of all, if there are no right or wrong answers,candidates cannot be defeated

• Unobvious By this, I mean not only that the problem is “deep” in

some nontrivial way, but that it often suggests an “obvious” firstimpression that is inevitably wrong

• Charming The best puzzles engage our intellects in ways that leave

candidates stimulated It’s hard to define what gives a puzzle this quality,but we know it when we see it Puzzles shouldn’t be arduous One goal

of puzzles in job interviews is to have fun while doing serious business

STRATEGIES FOR

SOLUTIONS

Employers who ask puzzles in interviews are often looking for peoplewho are good at divergent reasoning Divergent reasoning, as opposed toconvergent reasoning, is the process of finding previously undiscoveredsolutions to problems

The tools you need to solve problems with divergent thinking are nality, adaptability, fluency, and inventiveness Divergent thinkers examineall assumptions, stated and especially unstated The typical divergentthinker will usually explore many possible solutions before finding theoptimum one

origi-Convergent reasoning is likely to pick the first reasonable solution thatpresents itself It is often based on an unaware acceptance of unstatedassumptions And once having articulated a solution, convergent thinkerstend to stick with that one alternative, defending it like a dog with a chewbone The minds of convergent thinkers are trapped on one-way streets.Henry Ford’s famous slogan about model T Fords—“You can have anycolor you desire so long as it’s black”—is a classic example of conver-gent thinking And while there are occasions where convergent thinking

is desirable, the job interview is assuredly not one of them

LET THE FORCE BE WITH YOU

By “the Force,” I mean the conventions of puzzles and brainteasers Puzzlesolvers have evolved a set of agreements about how puzzles behave It’s a

7

world inhabited by characters that look like people but often act in waysthat would in the real world appear totally goofy

For example, there are a group of games called balance puzzles Inthese puzzles, the challenge is to find among a group the one thing thatweighs more or less than the others using the smallest number of weigh-ings Fair enough Let’s say it’s a coin In the real world, you might do allkinds of things with the coin You might saw it in half, melt it down, grind

it into powder, chew on it, heft it in your hands, do a chemical analysis,look on the Internet, bribe a jeweler, etc Some of these strategies may

be inspired; others may be stupid; none of them have a place in a balancepuzzle Puzzle conventions won’t tolerate such distractions So get intothe spirit of this world Embrace the constraints as offered and attend

to the abstracted geometry of the challenge

When puzzles are animated by humanlike creatures, it’s important to forgetpractically everything you know about complex, ambivalent human behavior.Puzzle creatures are simple, one-dimensional characters who exist only toserve the puzzle They usually have but one motivation Depending on thepuzzle, these characters are concerned only with maximizing money, escapingthe fire, moving items across a bridge, or behaving in predictable ways.Puzzle creatures understand probability, and when they are expected to actlogically, they never fail These creatures act instantaneously and are thor-oughly aware of the logical consequences of their actions Puzzle creaturesnever make mistakes, nor are they ever uncertain Puzzle creatures don’t have

an altruistic bone in their bodies; they never do anything because they arenice or it’s the fair thing to do When they act, it’s for their self-interest alone Even brilliant people can crumple under the pressure of a job inter-view But don’t despair Here are a few practical tips to make the taskeasier Heed what dozens of interviewers, recruiters, and job coacheshave to say about confronting puzzles and brainteasers

• The obvious answer is always wrong Depend on it—your first

thought is undependable The more obvious the answer seems, themore incorrect it is likely to be Almost all puzzles are deeper thanthey appear to be—that’s what makes them puzzles By all means,note the obvious answer Even share it with the interviewer, but alwayswith a measure of suspicion Now take the obvious answer and con-sider why it’s wrong

• Work the answer, not the question All the information you need is

al-ready there Nothing is missing

• Think first, and then speak Don’t be afraid of silence Take a minute

or even two to think about the problem “We want you to think, sothink,” a Microsoft interviewer observes Look like you think aboutevery answer Paradoxically, most interviewers reward deliberationmore than speed, so even if you think you know the answer before theinterviewer is finished with the puzzle, appear to think about it Yourfirst thought may be wrong And never interrupt the interviewer

• Break it down Smaller is more manageable If the puzzle involves

five marbles, see what would happen with two marbles

• Back-translate Repeat what you have just heard State the goal of

the problem You do this for several reasons: First, you get to hearthe case all over again Second, you show the interviewer that youwere listening And third, you do not end up answering the wrongquestion, which happens more often than you would think

• A dialogue is better than a monologue Be transparent Think out

loud Let the interviewer see you struggle with the problem Show thelogic path your mind is taking An interview is often structured like anexam, but a lot of answers can be worth partial credit If you’re talkingout loud, an interviewer knows where you are and can give you hints

• Honor Occam’s razor Favor the economical solution Occam’s razor

is the proposition that when two explanations account for a situation,the simpler explanation is better In the case of job interview puzzles,you can be pretty sure that the puzzles are less complicated than thesolutions you are considering Keep it simple

• We’re having fun, aren’t we? Use inclusive language—we and our—as

you solve the problem Inclusive language indicates your preference forteamwork and collaboration If you do it right, it gives the impressionthat you are already part of the team

• Ask questions; don’t just give answers Sometimes this means

chal-lenging the puzzle, but mostly it means asking clarifying questions.Make sure you are answering the problem being asked Use questions toestablish the scope of the problem before digging deep in one area

• Calculus is never required If you find yourself working a calculus

problem, stop immediately These puzzles never require more thansimple arithmetic In general, the more complicated the question, thesimpler the answer

• Work backward Often the solution is easier when you start from the

end of the puzzle and work backward

• All things being equal, give the interviewer a unique answer A good

way to stand out is to give the interviewer a solution he or she hasnever heard before

• Go for closure Often you will drift back and forth between two or

more equally attractive solutions You must pick and commit yourself.You don’t have to have a good reason, except for the need to move on.That’s just good business, and interviewers will respect you for it

• Ask for the answer If you don’t get the answer or the interviewer

indicates he or she has another answer in mind, ask for it Never fail

to turn the conversation into a learning opportunity

HELP! I’M TOTALLY STUMPED

The human brain is a marvelous organ It starts working the minute youare born and doesn’t stop until you are hit with one of these logic puzzles.When that happens, don’t worry The way you handle a puzzle you can’tsolve is almost as important as the way you handle a puzzle you can.The biggest mistake is to get all flummoxed and react like a deer inheadlights—too stunned to respond or survive Worse is to act like a drown-ing swimmer, lash out at the interviewer, and take him or her down with you

A good response does not always mean coming up with the right answer, but

it does mean showing good approaches to an unfamiliar problem

The best thing is to keep your sense of humor One very people-smartcandidate responded to a very difficult puzzle this way: “Hmmm one

of us doesn’t know the answer.” Another, referring to the popular TV

quiz show Who Wants to Be a Millionaire? in which contestants get to

make one phone call for help, asked: “How many lifelines do I have?” When you feel stuck, the first thing to do is to take a deep breath and askfor the puzzle to be repeated Now listen Sometimes the interviewer willsense something and provide a missing emphasis or detail Then repeat the

puzzle to the interviewer “Let me see if I have this right ” Then repeat

it again Sometimes saying a puzzle aloud to yourself once or twice revealssome opportunity for taking it to the next level Some candidates take time

to write the problem down Don’t let yourself be rushed

Then ask questions If there’s a detail you don’t understand, let theinterviewer know Own the difficulty “I’m having trouble with this prob-lem Can you help me understand ?” If none of this helps, ask for ahint “I’m sorry I seem to be stuck Can you give me a hint?”

Don’t let interviewers see you panic, but let them see you think outloud “You have to show them that your mind is cycling,” says formerMicrosoft developer Adam Barr “Have your internal dialogue out loud.Show them that you’re curious Let them see the answers you explore andthe dead ends you’re considering; invite them to go with you down theblind alleys Even if you never get right to the answer, they might beimpressed by your strategy.”

Finally, if you really are at a dead end and have nowhere to go, justadmit that you’ll need more time than you feel comfortable taking in ajob interview Don’t admit you can’t do the problem; just suggest youcan’t do it in the time frame of the interview Barr suggests wording like,

“I’m sorry I can’t work out the problem right here, but given time I’msure I can do it May I get back to you?” Even if you don’t get it, makesure the interviewer sees your curiosity and unflagging spirit “I know Ididn’t get it, but I’m really curious Can you tell me what the solution is?”This kind of closure replaces the sting of failure with a sense of optimismabout the next puzzle

Some candidates feel insulted by puzzles and brainteasers and treatthem like “illegal” questions Some simply say, “My policy is not torespond to questions like that.” Others respond with a challenge of theirown “What does that puzzle have to do with my ability to perform onthis job?” Most interviewers will respect your position They won’t hireyou, but they will respect your position If it’s respect you want, then

by all means pursue this course If it’s a job offer you want, then acceptthat for a candidate to engage in conflict on a job interview is counter-productive You may not like puzzles—you may find them insulting—but if you want to be considered for the job, there’s no alternative but

to take your best shot

REAL-WORLD REASONING PUZZLES

Sometimes the most common artifacts of our lives are the most puzzling How well do candidates observe the world in which they live? How curious are they about the phenomena, both natural and artificial, that fill the corners of our daily lives? How easily can they manipulate the tools and concepts that allow people to display the kind of intelligence people still call “common sense”? These puzzles test all kinds of skills— curiosity, observation, pattern recognition, for example—useful in business Interviewers believe that asking candidates puzzles like the ones in this chapter provide a glimpse into how candidates engage the world around them And it’s a bonus that many of these problems are just plain fun.

1 3

Why are manhole covers circular?

For years in the early 1980s, job candidates coming for their job views would yell upon arriving on the Microsoft campus, “Because theywon’t fall into the hole!” And the puzzle still shows up because it’s aclassic Interviewers get good clues about the candidate even if he or shehas studied the classic responses Here are the classic responses, in order

4 The manufacture of circular manhole covers is cheaper because

it requires less metal than the manufacture of covers of any othershape

5 Because manholes are circular!

The puzzle really extends beyond just picking an answer A date is expected to pick one or two responses and then defend them

candi-A Microsoft recruiter found the following response perfectly able for its grounding in moral values It’s always good to remind theinterviewer that these real-world problems are focused on preservinghuman safety:

reason-A circular cover is the only geometric shape that won’t fall into thehole and possibly injure someone below or create a hazard forsomeone above The slight lip on the manhole cover shaft preventsthe cover from ever falling in, no matter how it’s held A squaremanhole cover just wouldn’t work as well That’s because the diag-onal of a square is the square root of 2 times its side Should a squaremanhole cover be held near-vertically and turned just a little, itwould fall easily into the shaft The same is true with triangularshapes Circular shapes alone, because a circle has the same diam-eter in all directions, have the property we are looking for

If you want to go with another response, fine All these responses canwork, so pick one and be prepared for the objections and conversation.This puzzle is not about your engineering skills It’s about evaluating yourability to make a decision, communicate your reasoning, and defend it Avoid the temptation to be a smart aleck Yes, there are other shapesbesides circular that satisfy the condition that the cover be unable to fallinto the shaft But bringing the class of shapes referred to as Reuleauxpolygons into the conversation will not advance your chances unlessyou’re applying for a topology position

Extra credit: The reality is that not all manhole covers are circular DanHeller is a photographer who maintains a Web page of dozens of photos

of manhole covers (many with his shoes visible in the photo) that hetakes on his assignments around the world (http://www.danheller.com/manholes.html) While most of the manhole covers are indeed circular,clearly some municipalities prefer square and rectangular covers

2 ELIMINATE A STATE

This is one of the most popular questions still asked at Microsoft I’ve talked to dozens of people who have been asked this question In each case the interviewer seems to have a different “correct” answer in mind

If you had to eliminate one of the 50 U.S states, which one would you select? Be prepared to give specific reasons why you chose the state you did.

Don’t get hung up looking for a “correct” answer.” There is no correctanswer, unless you’re applying for a job with Microsoft, in which caseWashington State is definitely a nonstarter The best course is to reframethe question in some compelling way Another idea: Don’t start with thename of a state, but build some suspense by walking the interviewerthrough your logic and seeing where you end up together Humor alwayshelps There are dozens of creative answers Here are three of them

1 Well, I don’t want to be responsible for eliminating actual people

So I’d eliminate the political entity of a state by ceding it to

Canada, perhaps a state that shares a border with Canada, such

as North Dakota or Vermont Would I still be able to visit?

2 A similar approach calls for eliminating a state by actually bining it with one of its neighbors For example, Connecticutcan annex Rhode Island Or North and South Dakota can becombined to form the state of Dakota

com-3 I’d eliminate Wyoming [you get points for knowing thatWyoming is the least populous state], but only if the people andnatural attributes can be relocated to a theme park on the LasVegas strip

Candidates should be aware that some interviewers have an agendawhen asking this question and want candidates to come to a certain con-clusion One candidate reports that when he was asked this question, theinterviewer indicated the “correct” answer was to divide a square state(like Colorado or Wyoming) into several parts (presumably rectangular)and merge them with the neighbor states It turns out that the interviewerhad Colorado in mind as the ideal response Listen to how angry thecandidate was:

I thought I had covered every realistic possibility, but it boileddown to the interviewer being totally arbitrary At the end, it wasmore like “but what about splitting a state into multiple regions andcombining with all the neighbors” and “Colorado is rectangularand easy to divide” and so forth She had no comment either wayabout my other solutions and was totally stuck on dividing Colorado

I wasn’t sure if she wanted me to go into depth about satellitephotography and how it isn’t that tough with modern technology todivide an irregularly shaped state into equal parts, or admit thatdividing a state into multiple parts is a valid method that I skipped.She was very hung up on dividing equally area wise, as if populationdensities or other considerations didn’t matter We talked for a longtime, as a portion of the interview, about why I thought involvingmore states made it less likely for success, and she always seemed toignore this reasoning and return to dividing Colorado equally Somaybe the interviewer had some grudge against the state of Colorado,

was fascinated with that state’s rectangular shape or fascinatedwith easy geometric constructions (divide a rectangle into equalareas) Or was just being difficult for the sake of being difficult

Of course, the interviewer might have been testing how the candidatereacted if she pushed back on the candidate’s solution

3 A QUESTION OF BALANCE

This may seem like a trivial question, but Ed Milano, vice president

of marketing and program development at Design Continuum (www.dcontinuum.com), a product design consulting firm with offices

in Boston, Milan, and Seoul, finds it can be revealing

There are two people who want to balance on a seesaw The first person weighs 125 pounds The second person weighs 150 pounds How do they have to arrange themselves so the seesaw

is balanced horizontally? (See Figure 3.1.)

For Milano to make a job offer, he has to see how the candidate thinksunder stressful conditions, the environment that often describes life at aconsultancy that assists clients with make-or-break strategic design programs

“We never solve the same problem twice; every engagement is unique,”Milano says “So we’re looking for people who think about new things in

a new way, eager to move past established limits, and are confident enough

to push their teammates over their respective boundaries.”

125

150

?

Figure 3.1

What kind of response is Milano looking for? “At a minimum, thecandidate needs to communicate that the heavier person must sit closer

to the pivot point than the lighter person If the candidate gets up to drawthe configuration on the whiteboard, I see evidence that the candidateconceptualizes in images,” he says For a designer, that’s good

For a more elaborate seesaw puzzle, see puzzle 93

Solution: The heavier person must sit closer to the fulcrum

4 SALT AND PEPPER

This is a charming puzzle reminiscent of junior high school physics experiments Some recruiters like to use it during lunch interviews

Imagine that we sprinkle some salt on a piece of white paper Then we sprinkle some pepper over the salt Now, using only a plastic comb, how would you separate the salt from the pepper?

Hint: The answer will shock you.

Pull the comb through your hair several times This will create staticelectricity and attach a negative charge to the comb Now wave the combover the salt-pepper combination and the pepper, being much lighter, willattach itself to the comb The salt crystals, being much heavier, will be leftbehind

5 ROPE LADDER, RISING TIDE

This puzzle is almost too much of a trick question, but some interviewers find it a good way to start an interview Here, the interviewer is looking for a candidate who can “picture” a problem and thereby find the solu- tion obvious

A rope ladder hangs over the side of a ship The rungs are 1 foot apart, and the ladder is 12 feet long The tide is rising at 4 inches

an hour How long will it take before the first four rungs of the ladder are under water?

Hint: Buoyancy.

Candidates must be wary of problems that sound too easy There’s always

a trap No interviewer would offer a problem that requires such trivialmath, so the issue becomes a meta-problem: what’s the unstated puzzle?

In this case, the real puzzle is to realize that the frame of reference isinclusive The ship and the rope ladder act as a unit The rope ladder, beingattached to the ship, rises with the rising water, and if it is not submergednow, it will never be submerged no matter how high the water rises

an-A businessman devises a business plan for buying and selling coconuts He calculates that by buying coconuts for $5 a dozen and selling them for $3 a dozen, that in less than a year he will

be a millionaire His business plan and calculations are

accurate How is this possible?

Hint: Starting conditions.

When we hear puzzles like this, most of us start thinking in dot-comterms: elaborate rationalizations of why losing money is a sound businessproposition Some candidates respond by suggesting the businessman isbuilding market share by giving away product at below cost Or thathis strategy is to drive his competitor out of business so that he canthen control the coconut market All well and good, but these responsesalways assume a starting condition that the businessman has moremoney at the end of the experiment than before Perhaps the most elegantanswer is to conclude that the guy is perpetually going to lose moneywith this scheme, so that if he ends up a millionaire, he had to havestarted out as a billionaire

Solution: The businessman started out as a billionaire

7 HOLE IN THE IRON WASHER

This is a good warm-up question for a job interview Some candidates shoot themselves in the foot by making the question more complicated than

it is There’s something about the concept of holes that confuses people

What happens to the hole in an iron washer when the washer

is heated? Does the size of the hole decrease, increase, or stay the same?

Hint: What happens when metal is heated?

When a piece of metal is heated or cooled, it expands or contractsuniformly The effect is just the same as if the whole thing were scaled

up or scaled down The iron washer would expand when heated, aswould the hole in it

Solution: The hole gets larger

8 SIX WATER GLASSES

Another puzzle for interviewers who like puzzles that involve latables It can be presented using Figure 3.2 or using actual glasses of water or, as in this example, orange juice

manipu-Here are six glasses Three of these glasses contain orange juice (or water) Moving only one glass, can you arrange the glasses such that those containing the orange juice (or water) are next

to each together, without any empty glasses in between?

Hint: Pouring is moving

Figure 3.2

Solution: Pick up glass 2 (from left to right) and empty its contents

into the empty glass 5

9 EAST COAST, WEST COAST

This puzzle has a satisfying solution, but should be restricted to candidates who are expected to be familiar with the geography of the United States and the fact that East Coast and West Coast states are separated by two time zones—Central and Mountain Time—and when it is noon in, say, New York, it is 9 a.m in, say, California

Two people are talking long distance on the phone; one is physically in an East Coast state of the United States, the other

is in a West Coast state of the United States That is, the East Coast state borders the Atlantic Ocean; the West Coast state borders the Pacific Ocean The first person asks the other, “What time is it?” When he hears the answer, he says, “That’s funny I’m only one hour earlier than you.” How is that possible?

Hint: East is East and West is West and never the twain shall meet But they come closer than you think

As far as I can tell, there’s only one reasonable solution to this puzzle.One of the people is in eastern Oregon (a West Coast state that bordersthe Pacific, yet whose eastern portion is in Mountain Time) The other per-son is in western Florida (an East Coast state that borders the Atlantic,yet whose western portion is in Central Time) The difference betweenMountain and Central Time is one hour

Solution: One person is in eastern Oregon; the other is in western Florida.

Extra credit: The puzzle can be made even more challenging by ing the time for each person the same This is possible if it happens to be

mak-at the exact moment when daylight savings changes mak-at 2:00 a.m

10 HEADS-UP COINS

To some people, this puzzle is trivial; to others, its solution is hard

to fathom even after it is explained Most interviewers prefer to present